Abstract
Recently, a controller design method based on Sum of Squares programming has been developed for the control of discrete-time bilinear systems , and applications to power converters have been studied. In the present work, robustness issues arising in these designs are studied. First, the issue of change of operating point is addressed, and relevant stability analysis is developed. For linear systems, one can simply “shift the origin” of the deviation variables to obtain the same behavior for a new operating point. For nonlinear systems, in contrast, one will experience changed dynamics when applying the same controller at a new operating point (even after “shifting the origin”). New criteria are introduced to verify the stability of designed controller for other desired operating points. A related topic that is covered is the introduction of integral action in the bilinear controller design, giving offset-free control for persistent disturbances. The effectiveness of the proposed methods are evaluated based on time-domain simulations of a boost converter.
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Notes
- 1.
See [8] for the definition of \(K_\infty \,\) functions.
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Vatani, M., Hovd, M., Olaru, S. (2015). Robustness Issues in Control of Bilinear Discrete-Time Systems—Applied to the Control of Power Converters. In: Olaru, S., Grancharova, A., Lobo Pereira, F. (eds) Developments in Model-Based Optimization and Control. Lecture Notes in Control and Information Sciences, vol 464. Springer, Cham. https://doi.org/10.1007/978-3-319-26687-9_14
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